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On Self-Injective Perfect Rings

Published online by Cambridge University Press:  20 November 2018

Dolors Herbera and
Ahmad Shamsuddin
Dolors Herbera
Affiliation:
Department of Mathematics, American University of Beirut, Beirut, Lebanon
Ahmad Shamsuddin
Affiliation:
Department de Matemàtiques, Universitat Autonoma de Barcelona, 08193 Bellatera (Barcelona), Spain
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Abstract

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Let R be a left and right perfect right self-injective ring. It is shown that if the radical of R is countably generated as a left ideal then R is quasi-Frobenius. It is also shown that the same conclusion can be drawn if r(A ∩ B) = r(A) + r(B) for all left ideals A and B of R.

Keywords

16D5016L30Perfect ringsSelf-injective ringsQuasi-Frobenius ringsInjective EnvelopeSemi-local rings

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996, pp. 55 - 58
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Camillo, V., Modules whose quotients have finite Goldie dimension, Pac. J. Math. 69(1977), 337—338.Google Scholar
2. Clark, John and Huynh, Dinh Van, A note on perfect self-injective rings, Quart. J. Math. Oxford 45(1994), 13–17.Google Scholar
3. Faith, Carl, Algebra II, Ring Theory, Springer-Verlag, Berlin-Heidleberg, New York, 1976.Google Scholar
4. Hajarnavis, C. R. and Norton, N. C., On Dual Rings and Their Modules, J. Alg. 93(1985), 253–266.Google Scholar
5. Kato, T., Self-injective rings, Tôhku Math. J. 93(1985), 253–266.Google Scholar
6. Morita, Kitti and Tachikawa, Hiroyuki, Character modules, submodules of free modules and quasi-Frobenius rings, Math. Z. 65(1956), 414–428.Google Scholar
7. Osofsky, B. L., A Generalization of Quasi-Frobenius Rings, J. Alg. 4(1966), 373–387.Google Scholar
8. Utumi, Y., Self-injective Rings, J. Alg. 6(1967), 56–64.Google Scholar